Find a general expression for the slope of a tangent line to the indicated curve. Then find the slopes for the given values of x. Sketch the curves and tangent lines.

y=x2+2x+2; x=3, x=3.5

What is the general expression for the slope of a line tangent to the curve of the function y=x2+2x+2 at the pointP(x,y)?

mtan=

nothing

(Simplify youranswer.)

The slope at x=3 is

. (Simplify youranswer.)

The slope at x=3.5 is

. (Simplify youranswer.)

Sketch the curve y=x2+2x+2 and the line tangent to the curve at x=3. Choose the correct graph below.

Use the definition to find an expression for the instantaneous velocity of an object moving with rectilinear motion according to the given function relating s(in ft) and t(in s). Then calculate the instantaneous velocity for the given value of t.

s=4t22t; t=8

The expression for the instantaneous velocity of the object is

The instantaneous velocity after 8 s is ft/s.

Use the equation given below to calculate the slope of a line tangent to y=6x2+5x at P(4,76).