Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Let f(x) = −3+(3x² −x+1) ln(2√x−5)

(a) Find the derivative of f.

(b) Using the derivative and linear approximation, estimate f(9.1).

Expert Solution

Colby Messinger answered 2 years ago

Compute the derivative of each function a.) f(x)= x5/2 - 3x2/3 b.) f(x) = 3x- log7x+7...

Compute the derivative of each function a.) f(x)= x5/2 - 3x2/3 b.) f(x) = 3x- log7x+7 c.) f(x)= 8x6-5x3+3x2-11x+7

Using the definition of an anti-derivative, prove that x (ln x)3 – 3x (ln x)2 +...

Using the definition of an anti-derivative, prove that x (ln x)3 – 3x (ln x)2 + 6x (ln x) – 6x is an anti-derivative of (ln x)3 (must show all work)

Let f(x) = ln(x^2 + 9) Find the first two derivatives of f . Find the...

Let f(x) = ln(x^2 + 9) Find the first two derivatives of f . Find the critical numbers of f . Find the intervals where f is increasing and decreasing. Determine if the critical numbers of f correspond with local maximums or local minimums. Find the intervals where f is concave up and concave down. Find any inflection points of f

Let f(x) = ln x for 1 ≤ x ≤ 3. Write down the formula for...

Let f(x) = ln x for 1 ≤ x ≤ 3. Write down the formula for Simpson's Rule with n = 4 that approximates the integral of ln x on [1, 3]. Without doing numerical calculations, tell whether in approximating the integral of ln on [1, 3] by the Trapezoidal Rule with n = 8, the value T the Trapezoidal Rule gives is larger than, or is smaller than, the integral. Justify your answer.

. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative prove that f...

. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative prove that f '(x) = 6x + 5 Then, Find the tangent line of f(x) at x = 3 Finally, Find the average rate of change between x = −1 and x = 2

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

Question

Let f(x) = −3+(3x2 −x+1) ln(2√x−5) (a) Find the derivative of f. (b) Using the derivative...

Solutions

Expert Solution

Related Solutions

Compute the derivative of each function a.) f(x)= x5/2 - 3x2/3 b.) f(x) = 3x- log7x+7...

Using the definition of an anti-derivative, prove that x (ln x)3 – 3x (ln x)2 +...

Let f(x) = ln(x^2 + 9) Find the first two derivatives of f . Find the...

Let f(x) = ln x for 1 ≤ x ≤ 3. Write down the formula for...

. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative prove that f...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let F(x, y, z) = z tan^−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the...

Using the quotient rule find the derivative of the function in each case: I. f(x)=(x^2)/(x-5) ii....

Find the derivative Y=ln(3-2x)

a- Using the definition, find the derivative of the function y = 3x2-2x+32. b- Evaluate the...