Question

# The tangent to the curve $$y=e^{2x}$$ at the point $$(0, 1)$$ meets x-axis at?

A
(0,1)
B
(12,0)
C
(2,0)
D
(0,2)

Solution

## The correct option is C $$(2, 0)$$solution -  equation of curve is y=$$e^{2x}$$tangent to the curve is $$\frac{dy}{dx}=2e^{2x}$$$$(\frac{de^{x}}{dx}=e^{x})$$At points (0,1), the tangent  is $$(\frac{dy}{dx})_{(0,1)}=2e^{2(0)}$$$$(\frac{dy}{dx})_{(0,1)}=2e^{0}$$           $$[e^{0}=1]$$$$\frac{dy}{dx}_{0,1}=2$$when the slope is 2, and solve the tangent meets y axis the coordinate is 0,Hence the tangent meets the x axis at (2,0)Mathematics

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