The temperature of a person during a certain illness is given by the following e

Question

The temperature of a person during a certain illness is given by the following equation, where T is the temperature (degree F) at time t, in days. Find the relative extreme points and sketch a graph of the function T(t)= -0.1t^2 + 0.8t + 98.6. 0 lessthanorequalto t lessthanorequalto 8 What are the relative extreme points? Select the correct choice below and fill in the answer box to complete your choice (Simplify your answer. Type an ordered pair Use integers or decimals for any numbers in the expression Use a comma to separate answers as needed.) The relative minimum point(s) is/are The relative maximum point(s) is/are The relative minimum point(s) is/are and the relative maximum point(s) is/are Sketch a graph of the function. Choose the correct graph below.

Explanation / Answer

The given equation is quadratic with leading coeffcient negative, so parabola will open down and it will have only relative maximum at vertex.

Find the x coordinate of the vertex as

t= -b/2a

= -(0.8)/(2 * -0.1)

=4

When t=4, then

T= 100.2

So, the correct option is B

The relative maxima is at point (4, 100.2)

=================

Clearly graph A has maxima at midway of 90 and 110 that is at (4, 100.2).

Correct graph is A

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