Derivatives from tangent lines Suppose the line tangent to the graphof f at x = 2 is y = 4x + 1 and suppose the line tangent to thegraph of g at x = 2 has slope 3 and passes through (0, -2). Find anequation of the line tangent to the following curves at x = 2.a. y = f(x) + g(x)b. y = f(x) - 2g(x)c. y = 4f(x)

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Q: equation of the curve at every point of which the tangent line has a slope of -e-².

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Q: For f(x) = x, the instantaneous rate of change is known to be - 6 at x= - 3. Find the equation of…

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Q: Diffrentiation Formulas (derivative) Determine where, if anywhere, the tangent line to…

A: Let's find.

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Q: Formula for slope: f(x + h) – f(x) m = lim h→0 h 1. Given the function: f(x) = x² + 2x + 1 where x =…

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A: GIVEN DATA : Function y=f(x)=4+3-x       TO FIND : Equation of the tangent line at (x,y)=(-1,6) to…

Q: A. Equation of a Tangent Line: Find the standard (slope-intercept form) equation of the tangent line…

A: 1.  Given, fx = x2 - x + 2 = ySlope of tangent = dydx = f'x = 2x - 1At point 0, 2,f'x0, 2 = 2×0 - 1…

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Q: Assume that functions f and g are differentiable with f(-5)= 5, f'(-5)= - 3, g(-5)= -4, and g'(-5)=…

A: The detailed solution is as follows below:

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A: Please refer to the image below

Q: Slope of a tangent line Let f(x) = 2x 3 - 15x 2 + 24x. For what values of x does the line tangent to…

A: Here,f(x)=2x3-15x2+24x.Now,f'(x)=ddx(2x3-15x2+24x)       =6x2-36x+24

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A: This question is based on finding equation of tangent line.

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Q: Higher-order derivatives Find ƒ′(x), ƒ″(x), and ƒ‴(x).

A: To find the higher order derivatives.

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Q: Derivatives from tangent lines Suppose the line tangent to thegraph of f at x = 2 is y = 4x + 1 and…

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Q: 75. Derivatives from tangent lines Suppose the line tangent to the graph of f at x = 2 is y = 4x + 1…

A: The line tangent to the graph of f at x=2 is y=4x+1.

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: