SOLUTION: I need to know the steps to solve this problem. Hope you can help me. If f(x) = 3-x^2 how do I find the slope of the tangent line to the graph of f at (1,2) How do I find t

Question 5314: I need to know the steps to solve this problem. Hope you can help me.
If f(x) = 3-x^2
how do I find the slope of the tangent line to the graph of f at (1,2)
How do I find the slope-intercept equation of the tangent line to the graph of f at (1,2)
How do I graph f and the tangent line.
Thank you
Sue
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
gradient is found by differentiation.
f(x) = 3-x^2 so f'(x) = -2x --> this is the gradient at any point on the curve. You need to find the gradient at x=1, so then... f'(x) = -2(1) which is -2.

Now the tangent at a point (by definition) has the same gradient as the curve at that point, so the general form of the straight line is y=mx+c. We know m=-2, so we have y=-2x+c. We need to find c. To do that we need to know the x and y, which we do! (1,2)...so 2 = -2(1) + c --> c=4. So the tangent has equation y=-2x+4

When you say graph, you mean sketch it? or do it on graph paper?

Sketch --> need to know what shape the quadratic is..its x^2 term is -ve so that means it is a n-shape hump. Where does it cross the x-axis and the y-axis? You find out.

For the straight line... at the point on the curve where x=1, draw the tangent. the line should cross the y-axis at y=4. Remember this is a sketch, so not perfect artistic skills required, but at least try to get the general jist of the shapes and layout :-)

jon.

RELATED QUESTIONS
Hello, This is my first time on this site, but I have heard that you help students... (answered by stanbon)

If f(x) = x^2-4x+7 a) Find f(x) using the definition of the derivative. b) find the... (answered by longjonsilver)

I need to solve for y in this equation. can you show me the steps how to do this?... (answered by nerdybill)

I need to know how to do this problem, I've been stuck on it for awhile and I have to... (answered by ewatrrr)

I know how to do some of this problem but i need help. The problem is Find the... (answered by rothauserc)

Solve the equation. 1. 3a^2=-a+2 2. 3(x-3)=2(6-x) I am having alot of... (answered by stanbon,Nate)

Hello, I hope you can help! I've been working a problem for 2 hours, and my text book... (answered by checkley71)

Hi, I can do this problem by sight; meaning I know what numbers will work by looking at... (answered by stanbon,checkley71)

Hi, I can do this problem by sight; meaning I know what numbers will work by looking at... (answered by funmath)