Question

equation of an unknown graphic given by y= x^2 + 2x. the slope of the graph at x= 1 metre will be​

Answer 1

SOLUTION

GIVEN

The equation of an unknown graphic given by

y = x² + 2x

TO DETERMINE

The slope of the graph at x = 1

EVALUATION

Here the equation of the unknown graphic given by

y = x² + 2x

Differentiating both sides with respect to x we get

$\displaystyle\sf{ \frac{dy}{dx} = \frac{d}{dx} ( {x}^{2} + 2x)}$

$\displaystyle\sf{ \implies \frac{dy}{dx} = \frac{d}{dx} ( {x}^{2} ) + \frac{d}{dx} ( 2x)}$

$\displaystyle\sf{ \implies \frac{dy}{dx} = 2x + 2}$

Putting x = 1 we get

$\displaystyle\sf{ \frac{dy}{dx} \bigg|_{x = 1} = ( 2 \times 1) + 2}$

$\displaystyle\sf{ \implies \frac{dy}{dx} \bigg|_{x = 1} = 2 + 2}$

$\displaystyle\sf{ \implies \frac{dy}{dx} \bigg|_{x = 1} = 4}$

FINAL ANSWER

The slope of the graph at x = 1 is 4

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Find the slope of the chord of parabola y^2=4x whose midpoint is (1,1). Help with explanation

https://brainly.in/question/13409021

2. The equation of the curve in the form y = f(x) if the curve passes through the point (1, 0) and Find f’(x) = 2x-1 is

https://brainly.in/question/8817095