Use p(x) = In(x2 + x + 7) to answer the questions below. (a) Find p'(x) = (b) Find the equation of the tangent line to p(x) at x = 0. Use y as the dependent variable. (c) If the equation of the tangent line produces an underestimate for values of p(x) near x = 0, which of the following must be true near x = 0 ? Op'(x) is decreasing and p "(x) is positive Op'(x) is decreasing and p "(x) is negative Op'(x) is increasing and "(x) is positive

Q: a) If a derivative of the function is given as: f'(x) = 9x² + 16x - 7 i) Find the function f(x) in…

A:

Q: f(x) = (4x + 1)2;    (0, 1) (a) Find an equation of the tangent line to the graph of the function at…

A:

Q: 4. Find the slope of the tangent line to the graph f(x) = 3x² +4 at the point (2, 16) and determine…

A:

Q: The arch y = sin x, 0 ≤x ≤ π, is revolved aboutthe line y = c, 0 ≤ c ≤ 1, to generate the solid in…

A:

Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

A: Consider the equation as shown below: Here, And the object is to derivative of y.

Q: Given that f(x) = (x-2)/(x+3), find the slope of the tangent line at x = 2. %3D O a. 1/2 O b. -1/5 O…

A: