02.04 Differentiation: Definition and Fundamental Properties Mid-Module Check

Let f be the function defined as f of x is equal to the piecewise function of 2 for x is less than 4 and 4 times x minus 3 for x is greater than or equal to 4 period Which of the following statements is true? (6 points)

f is not differentiable at x = 4 because f is not continuous at x = 4.

Which of the following would not be a representation of the differentiable function f where f ′(1) = 2? (6 points)Which of the following would not be a representation of the differentiable function f where f ′(1) = 2? (6 points)

f of 2 minus f of 1 all over 2 minus 1

If g of x is equal to x squared divided by 2 minus 4x comma then g ′(x) is equal to which of the following? (6 points)

g ′(x) = x − 4

What is the average rate of change of the function f(x) = ex3 over the interval [−1, t]? (6 points)

the quantity e to the power of t cubed minus e to the negative 1 power all over the quantity t plus 1

Let f be the function given by f(x) = ln x2 + cos x. What is the value of f ′(−1)? (6 points)

−1.159