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Using the results of the previous exercise, determine how the concavity of $g$ is related to the concavity of $f$ Hint: there are four cases to consider.

$$\begin{array}{|l|l|l|}\hline f \text { is } & f \text { is } & g \text { is } \\\hline \text { increasing } & \text { Concave Upwards } & \text { Concave Downwards } \\\text { increasing } & \text { Concave Downwards } & \text { Concave Upwards } \\\text { decreasing } & \text { Concave Upwards } & \text { Concave Upwards } \\\text { decreasing } & \text { Concave Downwards } & \text { Concave Downwards }\end{array}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Missouri State University

Baylor University

Idaho State University

Lectures

03:13

For the following exercise…

03:26

Concavity Determine the in…

01:07

02:40

00:20

01:23

Let $F=f+g$ and $G=3 f-g$ …

01:17

03:58

01:58

suppose you define each of X to be one of Rolex ad gox over FX, where F and G are defensible functions on. And now you're asked to find the derivative of H evaluated before on the days we have is given in this table on the left Over here. So how do you go about doing this? Well, the first thing is to find h prime events. So this is just going to be the sum off the derivatives so that some beach the director of each party. So what's the Drew tip off? One of Rex? Well, one of Rex went differentiated is minus one of X wet on dhe. What's the drug of G over F? Well, this is just going to be the quotient rule again. So we've got from G prime of X FX minus as prime of X g of X allover. Vex squared. Okay, so and this is just the potion cruel. Okay, so we found the drifted. Now we've got to evaluate it, So let's look new. Goal H crime. Oh, full. We just used the information given in the table. So what is? It's just plug in the numbers now, so minus one over full squared ad G prime full that before minus F prime before cheer for pull over F four squared. OK, so this is going to be equal to minus one over 16. That g prime of four service of our table where we see that g prime of four is just nine. So sorry. Plus nine effort for zero. So that's that. F prime of four is minus three and g 04 is six. And then this whole thing is over f or four squared, which is zero squares. Now we're dividing by zero. So excellent. Let's see. This is then no defined Fantastic.

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