💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Find the value of $ c $ such that the line $ y = \frac{3}{2}x + 6 $ is tangent to the curve $ y = c \sqrt{x}.

03:22

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:42

Find the value of $c$ such…

00:51

What is the value of $ c $…

01:18

Find an equation of the li…

05:36

find an equation of the ta…

00:57

Find the points on the cur…

04:11

Find the equation of the t…

03:42

01:11

Tangent lines Find an equa…

02:48

Find the value of $c$ in F…

01:15

Find an equation of the ta…

it's lower. So when you read here So we're gonna start off by differentiating C square affects when we get C over two square root of X. This is for the line. Why equals three Half plus six is tangent to the curve, See skirt of X. So the slope off the line three over two should be equal to the derivative. So we see that this is equal to three over two. When we get our X value to be C square over nine, then we're going to solve the equation. So we get why is equal to three Have X Plus six we have. Why is equal to see square it of X. Don't we get three has X Plus six is equal to C square of X. Then we're going to simplify the equation by squaring both sides when we get nine over four Up Square plus 18 x was 36 is equal to see square necks, and we're going to simplify our equation even more. We got 9/4 c square over nine, which we got right here square plus 18 c square over nine plus 36 this equal to see square times C square over nine, and then we just simplify continuously. You see that? It's only positive. Um, Val, You see, since the only positive value sea gives a curve that intersects the line.

Numerade Educator

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Find the value of $c$ such that the line $y=\frac{3}{2} x+6$ is tangent to t…

What is the value of $ c $ such that the line $ y = 2x + 3 $ is tangent to …

Find an equation of the line tangent to the following curves at the given po…

find an equation of the tangent line at the given point.$$x y+x^{2} …

Find the points on the curve $c(t)=\left(3 t^{2}-2 t, t^{3}-6 t\right)$ wher…

Find the equation of the tangent line at the given point on each curve.$…

Find the equation of the tangent line at the given point on each curve. …

Tangent lines Find an equation of the line tangent to the following curves a…

Find the value of $c$ in Figure $3.16,$ where the line $l$ tangent to the gr…

Find an equation of the tangent line to the curve at the given point.$ y…