Participation activity 26 find the slope of the line tangent...

Name: participation activity 26 find the slope of the line tangent to y 6x at x 2 enter the exact answer include a multiplication sign between symbols for example a x enclose arguments of function 95772
Uploaded: 2020-02-18T01:40:22-08:00
Duration: 4 min 24 s
Channel: Christine Anacker
Description: participation activity 26 find the slope of the line tangent to y 6x at x 2 enter the exact answer include a multiplication sign between symbols for example a x enclose arguments of function 95772

PARTICIPATION ACTIVITY #26 Find the slope of the line tangent to $y = 6^x$ at $x = 2$. Enter the exact answer. Include a multiplication sign between symbols. For example, $a * x$. Enclose arguments of functions in parentheses. For example, $a * \ln(b * x)$. Slope=

Transcript

00:01 All right, we're looking at a walkthrough for question 25 out of the 3 .9 exercises.

00:05 Now, this section of questions are a little bit interesting because they're actually asking us for an equation of a line, a tangent line specifically.

00:15 So what you remember about derivatives is that a derivative will find you the slope equation at a very specific point.

00:25 But now i want to create a tangent line.

00:28 So i'm going to need to know what the slope of that tangent line is and then throw it into an equation as well.

00:35 So for these questions, i'm actually going to have to do two things.

00:40 So for the first one, i'm going to have to find the value of the point and then i'm going to actually have to find the slope at that point.

00:53 And then once i have that information, i can actually throw it in and calculate it from there.

01:01 So for the very first one here for 25, they want us to use the function f of x is equal to 6 the power of x, and they want us to find the tangent line when my value for x is 2.

01:16 So really i'm trying to solve what is the value of the function when f is 2.

01:23 And the value of that function for f is 2 is 6 squared and 6 squared happens to be 36.

01:30 So i have this point now that is at 2 and 36.

01:37 Now to find the slope of a tangent line at that point, i'm looking at the derivative.

01:44 So for this, i need to find the derivative of that function.

01:49 So to do that, i'm going to have to use my rules for when i have a power with a variable exponent.

02:00 So with that i keep my power the same, so a to the power of x, and then i'd have my natural log of my base.

02:10 So when i look at something like this question, 6 to the power of x would say the same, but then i'd multiply that by natural log of 6.

02:22 So that finds me the slope formula...

Question

PARTICIPATION ACTIVITY #26 Find the slope of the line tangent to $y = 6^x$ at $x = 2$. Enter the exact answer. Include a multiplication sign between symbols. For example, $a * x$. Enclose arguments of functions in parentheses. For example, $a * \ln(b * x)$. Slope=

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