Calculus
posted by Vincent .
There are two neighboring points P and Q on the curve f(x)=x^2
(a) Determine m(h), the slope of the straight line PQ
(b) The slope, S, of the tangent at P is defined as S=lim h>0 m(h). Find the value of S.
(c) Use this value of S to show that the equation of the tangent at P is y=4x4.
Respond to this Question
Similar Questions

Math
How can I determine a value of gradient from a graph if the line is curved. (not a straight line) This is where Calculus comes in If a graph is a curve, then the gradient (slope) of the curve is the slope of the tangent that you draw … 
Calculus
I have a two part question that pertains to a curve (r(x)) and its tangent line at x=3. We are given that at x=3, r(x)=8. In order to find the slope of the tangent line, we are given another point (on the tangent line): (3.2, 8.5). … 
12th Grade Calculus
1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3  9x + 5 at the point (3,5) [* for a. the answer that I obtained was y5 = 1/18 (x3) ] b.) What is the smallest slope on the curve? 
Calculus (pleas help!)
Find the slope of the tangent line to the ellipse x^2/36 + y^2/49 =1 at the point (x,y). slope =_______ Are there any points where the slope is not defined? 
calculus
1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve … 
calculus
Consider the curve defined by 2y^3+6X^2(y) 12x^2 +6y=1 . a. Show that dy/dx= (4x2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope 1 is tangent to the curve … 
Calculus
Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2yx) (b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2. (c) Show that there are now points (x,y) on the curve where the line tangent … 
Physics
can someone help i'm stuck on two questions? 
Calc AB
Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then: (Points : 1) A) The slope of the tangent line to the … 
calculus 1
The point P(2,1) lies on the curve y=1/(1x) If Q is the point (x, 1/(1x) find slope of secant line. these are the points 2, 1 1.5,2 1.9,1.111111 1.99,1.010101 1.999,001001 2.5,0.666667 2.1,0.909091 2.01,0.990099 2.001,0.999001 …