Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5. Which of the following statement is true?

Question

(it's a positive cubic function graphed with positive maximum at x = -1.5 and a negative minimum at x = 1.5)

f is concave up from x = 0 to x = 3.
f has an inflection point at x = 0.
f is concave down from x = -1.5 to x = 1.5.
None of these is true.

Which of the following functions grows the fastest as x grows without bound? (5 points)

f(x) = e^x
g(x) = ecosx
h(x) = (5/2) ^x
They all grow at the same rate.

Use Euler's Method with two equal step sizes to estimate the value of y(0.4) for the differential equation y ' = x + y, with y(0) = 1.
If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.48). (5 points)

Answer 1

since f"(x) = 0 at x = -1.5 and x = 1.5, and f"(x) < 0 in (-1.5,1.5), C is true

exponentials grow fastest, and the larger the base, the faster they grow. So, what do you think?

I'll let you apply Euler's method. It just involves extrapolating along the tangent line.

Answer 2

okay thanks for the first one!
and since 5/2 > e the answer should be C.
and the third one is 1.48?

Answer 3

oops I meant 5/2 < e so the answer would be f(x) not h(x)