12. Consider the function A(x) = sin(t2) dt. (a) Find A'(x) (b) Find the x-value of the first positive critical number of A(x) (c) At that first positive critical number you found in (b), does A(x) have a local max, a local min, or neither? Justify your answer

Q: Suppose you are given the derivative of some function p(t) as p '(t) = t.cos(10t) (a) Find the exact…

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Q: 10. (a) State the Fundamental Theorem of Calculus. -x sin t %3D (b) Let J(x) = S*. Evaluate: (i)…

A: Fundamental theorem of calculus

Q: c. List any critical values. d. Identify intervals of increase. e. Identify intervals of decrease.

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Q: 2. Find the derivative of the following functions and write the down the inner and outer functions…

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A: To Prove: Show that, given function is not differentiable at x = 3.…

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Q: 4)Given f(x) = 2x/(x2 + 1) a)Find the derivative. b)Find the critical numbers .

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Q: 1. Find the derivative f'(z) if it exists, and state where f(z) is analytic. *(i) ƒ(z) = (1 − 3z²)4.…

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Q: 0.6z Express the function h(x) = Ve' - 3 in the form h(x) = (ƒ o g)(x) where f(x) # x and g(x) ± x…

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Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In; x²+y

A: Given that a function f(x,y) is continuously differentiable on an open region, we can derive the…

Q: 5. Use the given derivative to find all critical points of f and at each critical point determine…

A: Given that, f'(x)=4x3-9x

Q: Evaluate f'(x) at x =2 given f(x)= (x²– 3)“

A: The given function is fx=14x2-34. Evaluate the differential of function at x=2.

Q: 6. Find the derivative of the following (express answer in simplest form): 1+ sinx a. f(x) = In…

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Q: (b) A "three-point formulas" for the derivative is 1 (-fo+ f2) 2h Apply it to f(x) = x' with xo,,x2…

A: The three point midpoint formula for  approximation error:                                     f1' ≈…

Q: 12 If f(t) = find f'(t). f'(t) =

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Q: 4. Find the second derivative for the following function a) )* 22 y3(x+ (an b) f(x)=/2x + at x= 2 c)…

A: See the attachment

Q: Let ø be a C' function, and suppose 00 $(x) = >, b,Un(x)., ø"(x) = ), cnUn(x). %3D n=1 =1 Express…

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Q: 1. Find f(x) if f'(x) = x/x and f(1) = 2

A: Given that: f'(x)=xx and f(1)=2

Q: Compute f'(a) algebraically for the given value of a. f (x) 2x – a2; a = -1 limp 0 (4 – h) = 0 limp…

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