Calculus Answers

A table of values of an increasing function f is shown.

0 5 10 15 20 25
-44 -37 -23 -7 17 35

Use the table to find lower and upper estimates for the integral I.

I = ______________(lower estimate)
I = ______________(upper estimate)

Use logarithmic differentiation to find the derivative of the function.
y = x^ln(x)

Find an equation of the tangent line to the curve at the point (1, 1).
y = ln (xe^x^2)

Differentiate the function.
y = 2x log7(√x)

Given f(x,y)=xye[sup]-(x^2+y^2)/2[/sup],& classify its stationary points.

Suppose that f(x) is continuous and differentiable on the interval [2,5]. Suppose also that f(2) = 9 and f’(x) ≤9. What is the largest possible value for f(5)?

Find a number c that satisfies the Mean Value Theorem for the function
F(x) = x ^3 -2x on the interval [1,2]

Round your answers to 4 decimal places

Find the number c that satisfies the conclusion of the Mean Value Theorem.

f(x) = 3x^2 + 2x + 1

[-1, 1]

Find the number c that satisfies the conclusion of Rolle's Theorem.

f(x)= √(x ) - 1/3 x

[0, 9]

A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function, given below, is often used to model the response curve, reflecting an initial surge in the drug level and then a more gradual decline. If, for a particular drug, A = 0.02, p = 3, k = 3, and t is measured in minutes, estimate the times, t corresponding to the inflection points. (Round the answers to three decimal places.)

S(t) = At^p e^-kt

t > 0