The derivative of a function f is given by f′(x)=0.1x+e0.25x. At what value of x for x>0 does the line tangent to the graph of f at x have slope 2 ?

Since the derivative gives you lines which are tangent to the graph f(x), you can find the slope of the line tangent through the equation of the derivative. Set 2 equal to the derivative and you will get 2=0.1x+e^0.25x (assuming you meant e^0.25x not e*0.25x in your question). Using a graphing calculator in order to find the answer graphically, find at what x are the two equations y=2 and y=0.1x+e^0.25x are equal. The result is x=2.287.

adioabiola adioabiola · Answer 2 · 2021-09-23T13:57:46+02:00

Here, we are required to determine at what value of x for x>0 does the line tangent to the graph of f at x have slope 2.

x = 2.29

A line tangent to the graph of f is given by the derivative of the function, f (i.e f')

However, this derivative has been provided in the question as ;

f′(x)=0.1x+e(0.25x).

The line tangent to the graph of f will therefore have a slope of 2 at point f′(x) = 2

Therefore, since f′(x) = 2 and f′(x)=0.1x+e(0.25x)

We can then say; 2 = 0.1x + e(0.25x).

This evaluation can then be carried out by the use of a graphing calculator and the value of x (for x > 0) is gotten to be;

x = 2.29

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