Question

tangent to the curve y = kx² at x= 2 makes an angle 45° to the + x-axis then K equals to
A. 0.67
B. 0.5
C. 0.25
D. 0.125

Answer 1

y=kx²
on differentiating we get,
dy/dx=k*2x

as we know that dy/dx= tan theeta =slope
then put that value of slope and you have to find the value of k at x =2
then,
tan45°=k*2*2
k=1/4 is the required ANSWER

Answer 2

$y = k {x}^{2} \\ tangent \: to \: curve \\ \frac{dy}{dx} = 2kx \\ at \: x = 2 \\ \frac{dy}{dx} = 4k$

now, tangent to curve makes 45 degree with x axis that means ,slope of line (dy/dx)=1 as
tan 45=1

$\frac{dy}{dx} = 1 \\ 4k = 1 \\ k = \frac{1}{4}$

=0.25
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