Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,400 questions

17,804 answers

1,438 comments

39,764 users

find all values of x where the tangent line to the graph of y=gx is parallel to y=15x-30

0 votes
consider the function

g(x)=(1/3)x^3+2x^2+20x+7
asked Sep 13, 2014 in CALCULUS by anonymous

1 Answer

0 votes

The curve is y = g(x) = (1/3)x3 + 2x2 + 20x + 7 and , the tangent line is parallel to y = 15x - 30.

So parallel lines have same slopes.

y = 15x - 30

Compare the above equation with y = mx + c.

Slope  is 15.

Therefore, slope of the tangent line is also 15.

y = (1/3)x3 + 2x2 + 20x + 7

Apply derivative on each side.

y ' = x2 + 4x + 20

Here y ' is slope of the tangent line.

x2 + 4x + 20 = 15

x2 + 4x  + 5 = 0

Compare it to .

Roots are

image

image

image

image

image

x values are imaginary.

There is no tangent line at real values of x.

answered Sep 13, 2014 by david Expert

Related questions

...