1. f(x)= x-ln(x) a) interval where the function increasing b) interval where the

Question

1. f(x)= x-ln(x) a) interval where the function increasing b) interval where the function decreasing c) interval where it concave up d) interval where it concave down 2. e^(x)+e^(-x) a) interval where the function increasing b) interval where the function decreasing c) interval where it concave up d) interval where it concave down 3. sin(theta) - 2cos(theta) on the interval [0, 2pi] a) interval where the function increasing b) interval where the function decreasing c) interval where it concave up d) interval where it concave down

Explanation / Answer

i will do the 1st part, rest you can do yourself f(x) = x - lnx f'(x) = 1-1/x f''(x) = 1/x^2 a) for increasing, f'(x) > 0 1 - 1/x > 0 1 > 1/x x>1 b) for decreasing x < 1 c) for concave up, f''(x) > 0 1/x^2 > 0 it is always positive, hence the curve is always concave up for all real value of x d) for concave down, f''(x) < 0 it is not negative, hence the curve is never concave down

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

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