Question

In the xy-plane, the graphs of the linear function L and the exponential function E both pass through the points (0,2) and

(1,6). The function f is given by f(x)=L(2) - E(2). What is the maximum value of f?
0.007

Answer 1

The maximum value of f is -8 such that f(x) = L(2) - E(2)

How to determine the maximum value of f?

From the question, we have the following parameters that can be used in our computation:

(0,2) and (1,6).

For the linear function, we hvae

f(x) = mx + c

Where

c = y, when x = 0

So, we have

L(x) = mx + 2

Using the point (1, 6), we have

m + 2 = 6

m = 4

So, we have

L(x) = 4x + 2

Calculate L(2), we have

L(2) = 4 * 2 + 2

L(2) = 10

For the exponential function, we hvae

f(x) = abˣ

Where

a = y, when x = 0

So, we have

E(x) = 2bˣ

Using the point (1, 6), we have

2b = 6

b = 3

So, we have

E(x) = 2(3)ˣ

Calculate E(2), we have

E(2) = 2(3)²

E(2) = 18

The maximum value of f is

Max f = L(2) - E(2)

Max f = 10 - 18

Max f = -8

Hence, the maximum value of f is -8