12. Suppose the PDF is given by f(x) = Cx² for 1 ≤ x ≤ 2, and zero otherwise. (a) Find the value of C. (b) Find the likelihood that a point selected at random with respect to this PDF is between 1.5 and 2. (c) With X (x) = x, find E(X) and Var(X).

Q: f'(x) = V= and f(1) = 3- I|

A: Explanation of the answer is as follows

Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

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Q: f(x) = (x² + In x)(x³ + 4x + 5) f(x) = (x2+5x) In x (Vx-6x)e* %3D

A: We have to find the derivative for each of the functions. 1. fx=x2+lnxx3+4x+52. f(x)=x2+5xlnxx-6xex

Q: A function f has f(25) = 22, f (25) = 2 and f" (x) < 0, for x ≥ 25. Which of the following are…

A:

Q: 2. Given f(x)=x-6, determine whether f'(6) exists.

A:

Q: 5) Suppose the function C(1), where trepresents the number of months from January 1, 2020,…

A: Given, C(t)  represents the energy cost to a manufacturing company, where t is the number of months…

Q: Let f(x) f'(2)= | ƒ' (6)= Lomm 7 Vx Evaluate each of the following: I

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Q: 7. If f(x)=√(1-1²)et² dt, on which interval is f decreasing?

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Q: Estimate Af. Use a calculator to compute the error and percentage error. Af = f'(a)Ax f(x) = V1+x a…

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Q: 6. Find f(x) dx if 5 for x 5

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Q: 6x erivative of f(x) equal to zero, calculate x*: f'(x*) = 0. Using the second derivative ther x* is…

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Q: Consider the function h(z), for which h(4) = -12 and h'(4) = -7. %3D h(z) Find f'(4) for the…

A: To Determine: find f'4 Given: consider the function h(x) for which h4=-12 and h'4=-7 also…

Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

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Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: 3. Differentiate. x²e* f(x)%3= x² + ex

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Q: 4. Consider f(x) = 6 + (x+3) ²/³. Find the extrema of this function using the first derivative test.

A: We have to find extrema by first derivative test.

Q: 7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c)…

A: This is a problem related to continuity of thr function. Please follow the procedure given below.

Q: 2. If If ƒ(x) = , find ƒ '(0). et

A: 2) The fx isfx=xex

Q: If f (3) = 5, g(3) = 2, f'(3) = 4, g'(3) = -4, and h(x) = 18. h'(3)? %3D what is 9(2). O 7 O -1 O…

A: f(3) = 5g(3) = 2f'(3) = 4g'(3) = -4

Q: Let f(x) = X x - a Find the value of a so that f'(1) = 1 - 4

A: This question is based on Quotient rule of differentiation.