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The diagram shows the graph of y = x/2 + 2/x, for 0 < x ≤ 8

(a) Use the graph to solve the equation

x/2 + 2/x = 3

(b) By drawing a suitable tangent, work out an estimate of the gradient of the graph where x = 1

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The diagram shows the graph of y x 2 2 x for 0 x 8 a Use the graph to solve the equation x 2

Answer :

Final answer:

(a) x = 1.8 and x = 6 are solutions to the equation.

(b) The slope of the equation is -3/2.

Explanation:

(a) To solve the equation x/2 + 2/x = 3 using the given graph

we can find the x-values where the graph intersects the line y = 3.

By looking at the graph, we can see that there are two intersection points: around x = 1.8 and x = 6.

From the graph, it appears that x = 1.8 and x = 6 are solutions to the equation.

(b To estimate the gradient (slope) of the graph where x=1, you can draw a tangent line at that point and find the slope of the tangent.

The slope of the tangent line at a given point is equal to the derivative of the function at that point.

First, find the derivative of y= x/2 ​ + 2/x

y'=1/2-2/x^2

When x=1

y'=-3/2

Learn more about Solving equations and finding gradients here:

https://brainly.com/question/28884694

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Rewritten by : Barada

Answer

0/6

2-3 I hope this helps you out!