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Question

A tangent is drawn to the curve y=x3+3x2+1 at (h,k) ; h>0. If the equation of tangent is y=9x4 then the value of h+k is 


A
5
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B
6
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C
4
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D
8
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Solution

The correct option is B 6
Equation of tangent 
y=9x4
Slope of tangent m=9
Given curve 
y=x3+3x2+1
Differentiating w.r.t. x,
y=3x2+6x9=3h2+6hh2+2h3=0(h+3)(h1)=0h=1 ; 3
h=1 
Putting in the tangent equation 
k=94k=5
Hence h+k=1+5=6

Mathematics

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