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`        a) Find p so that the curve y = x 3 + 2 x 2 + p x + 3 has one horizontal tangent line only.   b) Find the value of x where this tangent line occurs. `
7 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear nitin,

a) The horizontal tangent line has a slope equal to zero. We first need to find the first derivative of y and equate to 0.   y ' = 3 x 2 + 4 x + p = 0
For the above quadratic function to have one solution only, it needs to have its discriminant D equal to zero.   D = 16 - 12 p = 0
Solve the above for p to find   p = 4 / 3
b) To find the value of x where the horizontal tangent line occurs, we need to solve the above quadratic equation 3 x 2 + 4 x + p = 0 for x. It had the discriminant equal to zero, hence   x = - 4 / 6 = - 2 / 3

We are all  IITians and here to help you in your IIT  JEE preparation.  All the best.

Sagar Singh
B.Tech IIT Delhi

```
7 years ago
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