a.Find the first and second derivative of the function: f(x)=e^kx where k is a n

Question

a.Find the first and second derivative of the function: f(x)=e^kx where k is a non-zero constant. f '(x) = f ''(x) = Suppose that k is positive. b.Is the first derivative positive or negative? Negative Positive c.Is the second derivative positive or negative? Negative Positive d.Which of the following describes the graph of y=ekx? Increasing and concave up Decreasing and concave up Increasing and concave down Decreasing and concave down Suppose that k is negative. e.Is the first derivative positive or negative? Negative Positive f.Is the second derivative positive or negative? Negative Positive g.Which of the following describes the graph of y=ekx? Decreasing and concave down Increasing and concave down Increasing and concave up Decreasing and concave up h.Find the first and second derivative of the function: f(x)= ln x for x greater than zero. f '(x) = f ''(x) = i.Is the first derivative positive or negative? Negative Positive j.Is the second derivative positive or negative? Negative Positive k.Which of the following describes the graph of y = ln x? Decreasing and concave down Increasing and concave down Decreasing and concave up Increasing and concave up

Explanation / Answer

f(x)=e^kx f ' (x) = k*e^kx f '' (x) = k^2*e^kx the sign of f '(x) is depends on sign of constant k...If k is positive,f'(x) is positive or if k is negative-f ' (x) is negative. but f " (x) is always postive. increasing and concave up.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.