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Q: Distinguish Between Partial Derivative and Ordinary Derivative ?

A: ## Distinguish  Between Partial Derivative and Ordinary Derivative....

Q: find all relative extrema of thefunction. Use the Second Derivative Test whereapplicable. f(x)=x^{2}…

A: The given function,  f(x) =x2e-x .........................(1)  differentiate with respect to x

Q: Derivative of In |x| Differentiate In x, for x > 0, and differentiate In(-x), for x < 0, to conclude…

A:

Q: a. Find the function f given that the slope of the tangent line to the graph of f at any point…

A:

Q: Calculate the derivative 25 using Part 2 of the Fundamental Theorem of Calculus. 25 dt =

A: Given: ∫-1x6t2-t25dt

Q: Verify f(x). direction delta function 8(x - a)

A:

Q: Verify the tangent line approximation of the function at the given point. Then use a graphing…

A: To Find the derivative of the function :- To find the slope of the function at (0, 2)

Q: find all relative extrema of thefunction. Use the Second Derivative Test whereapplicable.f(x)=x…

A: Given function is: fx=xe-x Differentiating above with respect to x we get, f'x=ddxxe-x⇒f'x=e-x-xe-x…

Q: Discuss the relationship between the secant line, slope of the tangent line, derivative of a…

A:

Q: Show that no tangent line to the graph of f(x) = tan x has zero slope. What is the least slope of a…

A: Slope of tangent line to f(x)=tanx is given by f'(x)=sec2(x). sec(x)≠0 , so f'(x)≠0  This proves…

Q: Explain why the slope of the tangent line can be interpreted as an instantaneous rate of change. The…

A:

Q: Estimate the slope of the tangent line of the function y(t) = v4t + 1 at the point t = 1. (Use…

A:

Q: The slope of the tangent line to the graph of the function at the point. V The average rate of…

A: We have to check

Q: Where is the function defined by ƒ(x) = ex increasing?Decreasing? Where is the tangent line…

A: Where is the function defined by ƒ(x) = ex increasing? Decreasing? Where is the tangent line…

Q: Velocity is the first time derivative of position of time ylgn O ihi O

A: Velocity is the rate of change of displacement with time

Q: Integration is the reverse process of differentiation.

A: Given,            Integration is the reverse process of differentiation.To find : State true or…

Q: An orchard has an average yield of 36 bushels of apples/tree if the density is 22 trees/acre. For…

A: Let x be the additional number of trees to be planted to maximize the total yield.

Q: A farmer wants to fence in 800 ?t2 of land in rectangular plot to be used for different types of…

A:

Q: What is the least positive value for which the tangent function is undefined?

A: The tangent function is not defined where the cosine function is 0 because

Q: Estimate the slope of the tangent line of the function y(t) = V2t + 1 at the point t 1. (Use decimal…

A: We have to find the first derivative in order to find slope.

Q: Describe Leibniz’s notation for the derivative?

A: The derivative of a function is defined as the rate of change of a function y=f(x) with respect to…

Q: Identify the equation of the tangent line of the function: f(x) = 3x at x=2

A:

Q: se LONG METHOD DERIVATIVES to find the slope of the tangent line to the curve: (x) = -2x 1 at point…

A: Topic:- calculus and geometry

Q: Find the approximate derivative for f(x) = cos x on the interval [-7, 1] using forward difference…

A:

Q: derivative of arctan(1/x)

A: Solution:- we have to find the derivative of  y=arctan1x=tan-11x

Q: 3 + 2x +5

A: GIVENy=x3+2x+5   and x=2

Q: Fin derivative of the funclions. y=Log

A: The given function is: y=log3xx-12

Q: Explain in 200 words the relationship between the secant line, slope of the tangent line, derivative…

A: Given: secant line, slope of the tangent line, derivative of a function using the limit process,…

Q: 3e* at the point Estimate the slope of the tangent line of the function f(x) x=e (Use decimal…

A: Firstly, we find derivative of f(x) by using the result that derivative of e^x with respect to x  is…

Q: how do i estimate and list the value of x where f(x) has a horizontal tangent

A: Recall the following facts.

Q: equation of tangent line of f(x)=5x^3+1 at x=1 is * O y=15(x-1) O y=15 x-9

A: Given: The function f(x)=5x3+1 and a point x=1

Q: true or false?  Continuous functions have a tangent line at all points.

A:

Q: Explain theorem 10—First Derivative Test for Local Extreme Values?

A: According to the question, we have to expalin the theorem for first derivative test for local…

Q: Estimate the slope of the tangent line to f(x) = tan (x) at the point x = 4 (Use decimal notation.…

A:

Q: total derivative of the function f(x, y

A:

Q: 5. Find the average rate of change of the function f(x)= cos² x from x =- x = ". Use to - exact…

A: Rate of change=f(b)-f(a)b-a Given:  f(x)=cos2x, x=-π6,π4

Q: Acceleration is the first time derivative of velocity

A:

Q: sinh x O Compute the derivative of f(x) = (cosh x)

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Q: True or false The slope of th tangent line to a dfferentiable function f at the point (2,f(x)) is

A: The slope of the tangent line to a differentiable function f at the point (2, f(x)) is

Q: Estimate the slope of the tangent line of the function f(x)=3ex at the point x=e. slope of the…

A: Slope of the tangent line is given bythe first derivative of curve at given point.

Q: belongs derivative of a This Curue to the function Plot possible belonging to Curve the original…

A: Given: The graph of f'(x)

Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: Given f(x)=4x and x=2

Q: Using terms like "secant line" and "tangent line", explain how evaluating f(3+ h) – f(3) lim gives…

A: This is a problem related to derivation of the general formula of differentiation.

Q: Estimate the slope of the tangent line of the function f(x) = 7e* at the point x = e. (Use decimal…

A: We find f'(x)

Q: Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate…

A: Average rate of change of constant function fx=b Rewrite;              y=b…

Q: What are the intervals where the function has a positive first derivative? (d,e) (b,c) (c,d) (e,f)…

A: Recall the fact that the first derivative is positive if the function is increasing in that…

Q: Graphically, the instantaneous rate of change of a function at a specific x-value can be estimated…

A: Given: The below four statements are given: (a)Determining the slope of a single secant line on the…

Q: The maximum rate of change of the function 1 ----> at the point (1,-2) happens in direction of and…

A:

Q: Explain theorem 11—Second Derivative Test for Local Extreme Values?

A: Second Derivative Test for Local Extreme Values: Let f be a function defined on an interval I and…

Q: Find the derivative of the transcendental function. y = ex - cot x y' =

A: derivative of ex = ex dderivative of cot(x) = - cosec2(x)

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: