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Question

Set up an equation of a tangent to the graph of the following function.
At what points does the tangent to the graph of the function y=x+2x2 makes an angle of 135 with the x-axis?

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Solution

y=x+2x2
For ab angle of 1350, slope =tan135=1
y=1
(x+2)(x2)2+1x2=1
x2+x2(x2)2=14=(x2)2
x2=±4
x=4 or x=0
y(4)=4+242=3
y(0)=0+202=1
at point (0,1)and(4,3), the tangent makes an angle of 1350 with Ox axis$.

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