For the function with following rule, find f'(x) and sketch the graph of y = f'(x): { -x² + 3x+1 if æ >0 3x +1 if a < 0 For the function with the following rule, state the set of values for which the derivative is defined, find f'(x) for this set of values and sketch the graph of y = f'(x): f(z) = { + 2z +1 ifz>1 -2x +3 if z <1 For the function with the following rule, state the set of values for which the derivative is defined, find f'(æ) for this set of values and sketch the graph of y = f'(x): f(x) = {-z - 3x +1 ifr>-1 -2x +3 if æ < -1

Q: a).Find x value where the graph has a horizontal tangent line. f(x) = x^3 + x Using the fact that…

A: The given function is  f(x) = x3 + x Differentiate with respect to x , we get f'(x) = 3x2 + 1

Q: exp(x²) Vx²+1)( ¥2x* +3 18. f(x)= Vx*+1

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Q: Differentiate the function. y = (2x² − x + 1) (-x5 + 3) y' = 5

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Q: Find the function of the derivative f'(x)= -12x+5 and with the graph passing through (-2,5)

A: Given, f'(x)= -12x+5

Q: 2e* f (x) = x- 2e*

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Q: evaluate the derivative of the function at the given pointf(x)=-4/(2x2-3x)4 , (1,-4)

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Q: 3.25 The two-dimensional displacement field in a body is given by u₁ (X) = X₁ [X²X₂ +0₁ (20² + 30²X₂…

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