4. What is the exponential equation of the function shown? .4 -3 -2 a) f(x) = 3* – 2 b) f(x) = - 3 - 2 c) ƒ(x) = 3* + 2 -x d) f(x) = 3¯* – 2 -1 0 -2 2

Graph the quadratic function f(x)=2x24x3 first using the properties as we did in the last section and then graph it using transformations. Which method do you prefer? Why

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

1. Which pair of functions is equivalent? a. fAx) = - 8x - 5x – 3 g(x) = 8x + 5x + 3 c. Ax) = (-6x + 7x) + (8x? - x) g(x) = 2x2 + 6x %D

My question is in the picture

number 13

a) Select a point on the graph of y = −x² + 2x³ + 13x² − 14x − 24, where the roller coaster is going up and evaluate The First Derivative i. ii. b) Select a point on the graph of y = -x + 2x³ + 13x² − 14x − 24, where the roller coaster is down and evaluate The First derivative The Second Derivative ii. The Second Derivative c) At the highest, or lowest point of the coaster, the first derivative is zero. Does that mean that the second derivative at that point is zero? Explain using correct mathematical language and diagrams/graphs, and examples.

Determine the vertex of the function f(x)= lx-1l -1 How do I solve this?

A company that makes creepy dolls has found that their profit is given by the equation P=10q+4q²-300, where profit is in dollars, for q hundred creepy dolls produced. Currently, 12 hundred creepy dolls are being produced, and the number of creepy dolls being produced is increasing at a rate of 5 hundred creepy dolls per month. At what rate is the profit changing with respect to time? 5.

If f(x)=x^2-x-6