Consider a function y =f(t) with domain (0. 1, 4. 2). Use the graph of the derivative function, y=f'(t) ,given below to write down the t -value of the local maximum of f. If the function has no local maximum, explain why not

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A: according to the problem, we have

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A: Here given

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Q: Can you help me with this problem step by step?

A: To determine the derivative of given function.

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A: Consider the given function, fx=2x+1 differentiate with respect to x, f'x=ddx2x+1=122x+1·2=12x+1…

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A: The solution for the above question is as shown below.

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A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

Q: Find the derivative of the function.

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A: Please see the below picture for detailed solution.

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Q: find the derivative of y with respect to the appropriatevariable. y = sec-1 1t, 0 < t < 1

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A: →While calculating ∂f(x,y)∂y , consider 'x' as constant.→∂∂yuv = v∂u∂y-u∂v∂yv2

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Q: Calculate the derivative of the function g(x)=x∫√x(t2−t)dt at x=1.

A: using the fundamental theorem of calculus we find g'(x)

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