5. Consider the function f(x). f(x) = (2x² + 3x + 1 |x| sin(x - 1) + 1 if x < -1 if -1 < x < 1 if 1 < x -1, (a) Check if f(x) has a derivative at x = -1. If f(x) has a derivative at x = - then give the derivative. If not, explain why. (b) Check if f(x) has a derivative at x = 1. If yes, then give the derivative of f(x) at x = 1. If not, explain why.

Q: (a) tive of f(r) = r at z = a. Find the value of a given that lim, 8+h)* – 64 represents the deriva-…

A:

Q: 1 Suppose that f is a function given as f(x) We will compute the derivative of 2x +3 follows. First,…

A:

Q: b. f(x) = (x³ + 2x² + 4) (x 4 − 3) c. f(x) = = 3x²-6x+7 4x-1 d. f(x) = (4x³- 7x)7 -

A: To find the derivative of each of the following functions.

Q: = (x),! %D (b) Use part (a) to find the derivative of f(x). 4 (X)d – (4 + x)f (a) Compute the…

A:

Q: 23 The derivative of the function f(x) = xª + is 23 4x3 (x²) 23 4x3 + (w³) 23 4x3 + (x) 1 4x 23 O 4x…

A:

Q: If f(x) = 6x²e*, then what is the derivative of f(x) with respect to x? 6xex O 12xe* О бхе"(x + 1) O…

A:

Q: Consider the following functions. g(x) = x3 – x h(x) = (x3 – x)4 f(x) = 9(x3 – x)4 Find the…

A:

Q: Complete the table by finding the function g(x) and the derivative of g(x) and h(x), if possible.…

A:

Q: 8) Find the derivative of the function f(x) = (2x-1 x² + 1 if x ≤0 if x>0

A: Step 1:   Step 2: Step 3: Step 4:

Q: Let f(x) : Find f'(x). (Suggestion: rewrite the function before differentiating it.) х +

A: Solution

Q: Let f(x) and its linear derivative f'(x) be defined for all real numbers. Use the table of selected…

A: Step 1:Step 2:

Q: is even, odd function or neither

A:

Q: The slope of the tangent line at any point on the graph of f(x) = 7x2 + 4x is given by the…

A: Given f( x ) = 7x2 + 4x f'( x ) = limh→0f( x + h ) - f( x )h

Q: Write all answers with numbers rounded to two decimal places. In Calculus the derivative of…

A: