For a cubic function `y=f(x),f^(x)=4x` at each point `(x , y)` on it and it crosses the `x-a xi s` at `(-2,0)` at an angle of `45^0` with positive direction of the x-axis. Then the value of `|(f(1))/5|` is_______

Answer

-15

Explanation

f(x)=4x
f(x)=`2x^(2)+c`
given `f(-2)=1 or c=-7` `f(x)=2/3x^(3)-7x+C,f(-2)=0`
`0=-(16)/(3)+14+C or c=(-26)/(3)`
`therefore f(x)=2/3x^(3)-7x-26/32=1/3(2x^(3)-21x-26)`
`therefore f(1)=-15`