Question

Answer each of the questions below. (a) Find an equation for the tangent line to the graph of y = (2x + 1)(2x 2 − x − 1) at the point where x = 1. (b) Suppose that f(x) is a function with f(130) = 46 and f 0 (130) = 1. Estimate f(125.5). (c) Use linear approximation to approximate √3 8.1 as follows. Let f(x) = √3 x. The equation of the tangent line to f(x) at x = 8 can be written in the form y = mx + b. Compute m and b. Using this find the approximation for √3 8.1. 3. (5 pts) For each of the listed functions, determine a formula for the derivative function. It is important to be comfortable with using letters other than f and x. For example, given a function p(z), we call its derivative p 0 (z). (a) f(x) = x 101 + x − k x (b) g(x) = 8x 12 − 3 7x + π sin(x) − 2 sec(x) (c) p(z) = cos(z)+z sin(z)+z (d) h(t) = (t + 1) sin(t) + t 2 tan(t)+1 (e) c(r) = r 2 csc(r)+13

Answer #1

1.) Find the equation of the tangent line to the graph of the
function f(x)=5x-4/2x+2 at the point where x=2
2.) Find the derivative: r(t)=(ln(t^3+1))^2

find an equation for the line tangent to the given curve at the
point defined by the given value of t.
x sin t + 2x =t, t sin t - 2t =y, t=pi

a) Find the equation of the tangent line to f(x) = e –x at the
point (1, e –1).
b) Find the equation of the tangent line to f(x) = 3x2 – 2x + 5 at
x = 2.

Find the equation of the tangent line to the function f(x) =
ln(7x) at x=4.
(Use symbolic notation and fractions where needed. Let y = f(x)
and express the equation of the tangent line in terms of y and
x.)
equation:

Find the equation of the tangent to the graph at the indicated
point. HINT [Compute the derivative algebraically; then see Example
2(b) in Section 3.5.]
a.) f(x) = x2 − 3; a = 8
b.) f(x) = x2 − 8x; a = −1

Suppose that f(x) = (2x)/((4-2x)^3)
Find an equation for the tangent line to the graph of f at
x=1.
Tangent line: y =

Use
the limit definition of the derivative to find the equation of the
tangent line to f at x = 3 3 f(x) = 1/(x + 1) Show all of your
work

f(x)=1/2x ln x^4, (-1,0)
a) find an equation of the tangent line to the graph of the
function at the indicated point.
b) Use a graphing utility to graph the function and its tangent
line at the point.

3. Find the equation of the tangent line to the curve 2x^3 + y^2
= xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3
= 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x
cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your
knowledge of the derivatives of sine/cosine with derivative
rules.
7. Use implicit differentiation to show that...

Find the equation of the tangent line to the curve
r = 2 sin θ + cos θ
at the point
( x 0 , y 0 ) = ( − 1 , 3 )

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 29 minutes ago

asked 40 minutes ago

asked 43 minutes ago

asked 48 minutes ago

asked 52 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago