# HS Calculus

posted by .

Definition of the derivative to calculate f'(x) if f(x) = square root 2x. Find the equation of the tangent & normal line to the graph of f at x=2.

Tangent line - y=2x-x
Normal line - y = 1/2x +3

I do not know whether these are the correct answers.

• HS Calculus -

no.

y = √(2x) = (2x)^(1/2)
y' = (1/2)(2x)^(-1/2)(2) = 1/√(2x)
when x=2, y = 2, y' = 1/2

so the tangent line is
y = (1/2)x + b
which at (2,2) is 2 = (1/2)(2) + b
b = 1

so the tangent equation is y = (1/2)x + 1

the normal would have slope of -2
so at (2,2)
2 = -2(2) + b
b = 6
the normal has equation y = -2x + 6

• HS Calculus -

Thank you . I think that I understand alittle better. It is oblivious that I do not understand this material.

• HS Calculus -

I have one more that I really am lost at.
Question - find the points on the graph y=2x^3-3x^2-12x+20 at which the tangent is parallel to tthe x-axis. I do not even know where to begin. We were told we could use the shortcut for this one.!

Thanks again

• HS Calculus -

If a tangent is parallel to the x-axis, wouldn't it have a slope of zero?

And isn't the slope represented by the first derivative?

so differentiate, set that equal to zero and solve for x

find the y's for those x's and simply say

y = (whatever the y values are)

let me know if you don't get y = 0 and y = 27

## Similar Questions

1. ### Calculus

find the equation of a line tangent to the graph of y = x / (square root of 5x^s +4), at x = 1. am i suppose to take the derivative?
2. ### Calculus

If f(2)=3 and f'(2)=5, find an equation of a. The tangent line b. The normal line to the graph of y=f(x) at the point where x=2 So I plotted (2,3) and (2,5)...but that's not getting anywhere... Thanks
3. ### calculus

use the definition of the derivative to calculate f'(x), if f(x)= SQRT(2x) and find the equations of the tangent line and the normal line to the graph of f at x=2
4. ### College Calculus

Let f(x) = 3x^2 - 2x + 1 a) write an equation of the line going through the points (1, f(1)), and (2, f(2)). b) Find a point on the graph of f where the tangent line to the graph has the same slope as the line in part (a). Write the …
5. ### calculus

Find an equation of the line that is tangent to the graph f and parallel to the given line Function: f(x)= 1/ square root of x Line: x+2y-6=0
6. ### Calculus

If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x …
7. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
8. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
9. ### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?
10. ### Math (equation of tangent line)

Consider the implicit equation 2xy-1=(x+y+1)^2 a) Compute and solve for the derivative dy/dx as a function of x and y. b) Find the equation of the tangent line to the graph of the above when y=-1. For part a, I found the derivative …

More Similar Questions