Find the derivative of the equation f(x)=x^2+7x-2 at x=0

Answer 1

Hello Ava

Find the derivative of the equation f(x)=x^2+7x-2 at x=0

 Add answer

x² +7x -2 = y = f(x)

dy/dx= d/dx(x²+7x-2) =2x+7 - 0

Plug in x= 0

it is 7

So dy/dx for x=0

=7

Answer 2

For f(x) = x² + 7x − 2, obtain the derivative f'(x) by moving the exponent of x² to the left of the x and placing (2 − 1 or 1) as the new exponent: 2x^(2-1) or 2x¹ or 2x.

Then, for 7x or 7x¹, differentiate by placing the exponent 1 to the left of the 7 and placing (1 − 1 or 0) as the new exponent: 1•7x^(1-1) or 7x⁰ or 7(1) or 7.

Finally, obtain the derivative of 2 by noting that 2 is an exact fixed number with no variability involved; a function equal to 2 has a graph that is a horizontal line, all of whose points have ordinates or y-values of 2.

The slope (or derivative) of this flat horizontal line would then be equal to 0, since the line does not ascend or descend. That is to say, the horizontal line has "zero slope". (Note that a vertical line in Mathematics is said to have "no slope".)

Placing the 3 partial answers together then gives (as the derivative d[x² + 7x − 2]/dx) a result of 2x + 7 − 0 or 2x + 7.

At x = 0, 2x + 7 equals 2(0) + 7 or 7.