Given the function f(x)=3x-1 what would be the equation of the function after the following transformations 2f(2x+1) a. 2f(2x+1)=6√√2x + 1 b. f(x)=6√/2x c. 2f(2x+1)=6/2x d. f(x)=6√√2x + 1

Find the points of inflection of the functionf(x)=3√x2(x+1).

Differentiate the given function f(x) = ³√x⁴ - 3 ⁵√x² +8

Use the following functions to evaluate/ perform the indicated operations. g(x) = -x² - 7 h(x) = -√√x 8. f(-3) = f(x)=3x-5 11. g(2a-3)= 9. g(-4)=_ 12. (fog)(-5) = p(x) = -4 10. p(-7). 13. (g- h)(25) =

Suppose that f(x)=4x−(2√x+91x2)f(x)=4x−(2x+91x2). Evaluate each of the following:f′(2)f′(2) = f′(4)f′(4)

steps. For the function h(x) = −2x³ - 4x + 3√x, calculate h'(x), h'' (x), and h''' (x) . Show all 2 h(x) = -6x² - 4+ 3 ī h"(x) = 4 (+6x²-4 + 3 = 2√x h(x) = -2x 3-4x +3√3 dx 2√x h "(x) = 2 ( 6x²)_ _d (4) + d( 2 dx dx h"(x) = -60 • 2x+0-3x21 2. h²(x)= x (-2x ³ - 4x + 3√x 2 3 n'(x) = d (-2x ³) + d (-4x) + d (3√x) dx dx h'(x) = (2) (3x²+4+3 (1) 2 |h²(x) = -6x ² - 4 + ²³ 3 25 2√√x √ 3|hx)=12x-3 4x-√7 hly--12x n(x) = d (~3) • (4x√7) - d (4x√x) = (-3) 4 = 4• zx : -12 dx 4XXX 4x -3 x 1 4x X2 4/2 Ex -6.1X (2 h" (x) = -67-3x • 2 (₁x) (2√x)2 h(x=-12x-3) -3 4x√x

Eliminate the square root at the denominator of the function: f (x) = (7 - √x - 6) / (7 + √x − 6), with x≥6 Your answer should be in the form: f (x) = (A + B√x− 6) / (C - x), with x ≥ 6, x ≠ C where A is a function of x but B and C are constant numbers. What are the values of A, B and C? (Pay special attention to the signs!) A = __________, B = __________, C = __________.

A kid launches a bottle rocket off of a launch pad. The rocket's height above the ground (in feet) tt seconds after its launch is given by the function, h(t)=−t^2+16t+4=−(t−8)^2+68=−(t−(8+2√17))(t+(8+2√17)) At what time does the rocket reach its maximum height? What is the heigh of the launch pad that the rocket was launched from? How long does it take until the rocket land on the ground?

b. f(x+5)-1/2 √2+5

50) Find the equation of the line tangent to f(x)=3x² -5x+8 at x = 2. Answer in slope-intercept form. 51) Find the equation of the line tangent to f(x) = 4√x+5 at x = 4. Answer in slope-intercept form.