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Area between Two Curves

If the curves...

Question

If the curves $y = x^{3} + a x$ and $y = b x^{2} + c$ pass through the point $(- 1, 0)$ and have common tangent line at this point, then the value of $a + b$ is?

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Solution

The correct option is B $- 2$
As the curve pass through the point $P (- 1, 0)$
$0 = - 1 - a$
$⟹ a = - 1$
$0 = b + c$
Common tangent at this point
$\frac{d y}{d x} = 2 b x$ and $\frac{d y}{d x} = 3 x^{2} + a = 3 - 1 = 2$
$2 b x = 2$
$- 2 b = 2$
$b = - 1$
$a + b = - 2$

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If the curves y=x3+ax and y=bx2+c pass through the point (−1,0) and have common tangent line at this point, then the value of a+b is?

The correct option is B −2As the curve pass through the point P(−1,0)0=−1−a⟹a=−10=b+cCommon tangent at this point dydx=2bx and dydx=3x2+a=3−1=22bx=2−2b=2b=−1a+b=−2

If the curves $y = x^{3} + a x$ and $y = b x^{2} + c$ pass through the point $(- 1, 0)$ and have common tangent line at this point, then the value of $a + b$ is?

The correct option is B $- 2$
As the curve pass through the point $P (- 1, 0)$
$0 = - 1 - a$
$⟹ a = - 1$
$0 = b + c$
Common tangent at this point
$\frac{d y}{d x} = 2 b x$ and $\frac{d y}{d x} = 3 x^{2} + a = 3 - 1 = 2$
$2 b x = 2$
$- 2 b = 2$
$b = - 1$
$a + b = - 2$