Question

If x be real find the maximum value of 7+10x-5x^2

Answer 1

To find the maximum value of this equation you differentiate the whole equation by x.
$\frac{d}{dx} ( - 5 {x}^{2} + 10x + 7)$
We get (-10x+10)
Now we equate this equation by 0 and find the value of x.
-10x+10=0
or, x=1.
Hence, we have either minima or maxima at 1. to confirm either of the one we differentiate it again by x.
$\frac{d}{dx} ( - 10x + 10)$
We get -10. Note:- When double differentiation of any polynomial comes out as a negative, it is maxima, else minima.

Hence, the Maximum value of the equation, putting x=1, is
$- 5( {1}^{2}) + 10.1 + 7 = 12$
Therefore, maximum value is 12.
thank you.