Algebra 2 H Secants and Tangents

What is the average rate of change  $f\left(x\right)=x^2+5x$  over the interval [1,5]?

• 11

• -11

• 44

• -44

What is the slope of the secant line that intersects the graph  $g\left(x\right)=\frac{x}{x^2+1}$  at x = 2 and x = 3?

• 0.1

• -0.1

• 0.7

• -0.7

Estimate  $g'\left(2\right)$ .

•  $\frac{1}{4}$  

•  $3$  

•  $-3$  

•  $-\frac{1}{4}$  

•  $0$  

Compare: h'(1) ______ h'(6)

• $<$

• $>$

For function f, we are given f(3) = -2 and f'(3) = 4, What's the equation of the tangent line to the graph of f at x = 3?

• $y-3=4\left(x+2\right)$

• $y+2=4\left(x-3\right)$

• $y-4=-2\left(x-3\right)$

• $y-3=-2\left(x-4\right)$

The tangent to the graph of function f at the point (2,3) passes through the point (7.6). Find f'(2).

• $-\frac{5}{3}$

• $\frac{5}{3}$

• $-\frac{3}{5}$

• $\frac{3}{5}$

What is the average rate of change of  $g\left(x\right)=7-8x$   over the interval [3,10]?

• 8

• -8

• 7

• -7

Estimate g'(4).

• -3.2

• 3.2

• -0.75

• 0

• 0.75

The tangent line to the graph of function g at the point (-6, -2) passes through the point (0,2). Find g'(-6).

• $\frac{3}{2}$

• $-\frac{3}{2}$

• $\frac{2}{3}$

• $-\frac{2}{3}$

For a function h, we are given that h(-2)=-5 and h'(-2)=-9. What's the equation of the tangent line to the graph of h at x=-2?

• $y+9=-5\left(x+2\right)$

• $y+2=-5\left(x+9\right)$

• $y+5=-9\left(x+2\right)$

• $y+2=-9\left(x+5\right)$