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Q.

If the slope of the tangent drawn to the curve $y = e^{a + b x^{2}}$ at the point P(1,1) is -2, then the value of 2a-3b=

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a

7

b

8

c

6

d

5

answer is A.

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Detailed Solution

$\begin{array}{l} y = e^{a + b x^{2}} \\ At x = 1, y = 1 \\ 1 = e^{a + b} \Rightarrow a + b = 0 \\ {\frac{d y}{d x}|}_{(1, 1)} = e^{a + b x^{2}} 2 b x \\ \Rightarrow e^{a + b} \cdot 2 b = - 2 \\ \Rightarrow b = - 1 & a = 1 \\ 2 a - 3 b = 5 \end{array}$

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