Let f(x) = 4×2. Compute f(3 + h).

(Use symbolic notation and fractions where needed.)

f(3 + h)

=

Compute

f(3+h)-f(3)

h

(Use symbolic notation and fractions where needed.)

f(3+h) – f(3)

h

=

Compute f'(3) by taking the limit as h +0.

(Give your answer as a whole or exact number.)

f(3) =

Let f(x) = 4×2 – 3x – 7. The secant line through (2, f(2)) and (2 +h, f(2 + h)) has slope 4h + 13. Use this formula to

compute the slope of the given lines.

(a) Find the slope of the secant line through (2, f(2)) and (3, f(3)).

(Give your answer as a whole or exact number.)

mi

=

=

(b) Find the slope of the tangent line at x = 2 (by taking a limit).

(Give your answer as a whole or exact number.)

m2

X – 3

f(2)-f(3)

Find the difference quotient

when f(x) = 1 – 3x + 6×2. Simplify the expression fully as if you were going to

compute the limit as x + 3. In particular, cancel common factors of x – 3 in the numerator and denominator if possible.

(Use symbolic notation and fractions where needed.)

f(x) – f(3)

2 – 3

=

Use your result to compute the derivative.

(Give your answer as a whole or exact number.)

f(3) =

Find the equation of the tangent line at (2, f(2)) when f(2) = 6 and f'(2) = 2.

(Use symbolic notation and fractions where needed.)

equation:

Use the limit definition to calculate the derivative at z = a of the linear function k(z) = 15z + 19.

(Give your answer as a whole or exact number.)

k'(a) =

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