5. Let f'(x) = ²3-4. Assume the domain of f is (-∞, -1) U (-1,0). Note you are being given the derivative of f but asked questions about f itself. x+1 (a) Find the intervals where f is increasing and decreasing. Identify the relative extrema. (b) Find the intervals where f is concave up and down and identify any inflection points. (c) Assume limx→-1-f(x) Sketch a graph of f. = lim,→-1+ f(x) = ∞ and f(-4): = 1 and f(1) = 2.

Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

A: Given,

Q: 75 2. Let f(x) = 2+ 3x² on the interval 15z5 50. (a) Use the approximation formula to estimate the…

A: (a) The approximate derivative of the function is given by f'(1+h)≈f(1+h)-f(h)h, where 1≤h≤49 and is…

Q: # 41) Use the definition of derivative to find f(r) and "(r) for (r)= 1+ 4r- r

A:

Q: Assume that the first derivative of a function y = f(x) is given by (x² + 1) (x² – 4)² ' Thus, which…

A: According to question that :y'=-x2+1x2-42

Q: 9. Use the definition of derivative to find the derivative of f(x) = x² – 3x.

A: We need to evaluate the derivative of the function f(x) using definition of the following function…

Q: Exercise 5: For the following graphs, sketch a graph of the derivative (i.e., you are given f;…

A: Consider the given curve of f(x).

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Q: Let f be a function defined on the closed interval -4sxs4. The graph of f', the derivative of f, is…

A: Let's find.

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Q: 2r +3 Let f(r) = (a) Find the derivative of f at r = 3 using the definition of the derivative as a…

A: f(x) = 2x+3/x  a) find the derivative  b) find the equation of tangent line at x= 3

Q: what is a and b please?

A: Use chain rule to find the h ' (x) and g ' (x).

Q: Set up and evaluate the triple integral in spherical coordinates needed to compute the volume of the…

A:

Q: Let f(x) = 4x² - 15x + 13 The slope of the tangent line to the graph of f(x) at the point (2, -1) is…

A:

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A:

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A: The derivative of a function y=f(x) is given by f'x=limh→0fx+h-fxh. The given function is fx=x+5.

Q: Is there anything special about the derivative of an even differentiable function of x? Give reasons…

A: The derivative of an even differentiable function is odd.

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A:

Q: 6. Consider the DERIVATIVE f' graphed below. Sketch a possible graph of the original function f on…

A: