At what points on the graph of

chechemuaen7

chechemuaen7

Answered question

2022-03-17

At what points on the graph of f(x)=2x39x212x+5 is the slope of the tangent line 12?

Answer & Explanation

i1a6ldihq

i1a6ldihq

Beginner2022-03-18Added 4 answers

The derivative of a function gives us the slope of a tangent line for a specified value of x
f(x)=2x39x212x+5
implies
f(x)=6x218x12
and we are asked to find when this is =12
6x218x12=12
x23x4=0
which factors as
(x-4)(x+1)=0
when x=4
f(x)=2(4)39(4)212(4)+5
=-59
when x=-1
f(1)=2(1)39(1)212(1)+5
=6
So f(x) has a tangent with slope 12 at
(4, -59)
and
(-1, 6)

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