Calculus
posted by Allison .
Let f(x)=21−x^2
The slope of the tangent line to the graph of f(x) at the point (−4,5) is ______ .
The equation of the tangent line to the graph of f(x) at (−4,5) is y=mx+b for
m=______
and
b=_______.

Calculus 
Steve
f(x) = 21x²
f'(x) = 2x
f'(4) = 8
The line through (4,5) with slope 8 is
(y5)/(x+4) = 8
y = 8x +37
I think that's enough of these.
Respond to this Question
Similar Questions

calculus
Find an equation for the tangent line to the graph of f at the point P = (−1, f(−1)) when f(x) = 4x + 1 3x + 1 
calculus
Write the equation of the tangent line to the curve at the indicated point. As a check, graph both the function and the tangent line. f(x) = x7 − 7 at x = −1 7 x7 
Math
The point P(8, −3) lies on the curve y = 3/(7 − x). (a) If Q is the point x, 3/(7 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of … 
calculus
To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (64, 8), we know that (64, 8) is a point on the line. So we just need … 
Calculus
Find the equation of the tangent line to the graph of 4y^2− xy − 3 = 0, at the point P=(1,1) 
Calculus
Sketch a graph of the parabola y=x^2+3. On the same graph, plot the point (0,−6). Note there are two tangent lines of y=x2+3 that pass through the point (0,−6). The tangent line of the parabola y=x^2+3 at the point (a,a^2+3) … 
MathsCalculus
If f(2)=1 and f(2+h)=(h+1)3, compute f′(2). If f(−1)=5 and f(−0.9)=5.2, estimate f′(−1). If the line y=−3x+2 is tangent to f(x) at x=−4, find f(−4). Your answer should be expressed as … 
calc
Find an equation of the tangent line to the graph of f(x) = (x3 − 3x2 + 1)(2x4 − 1) at x = −1. 
calculus
f(t) = − 4 t2 − t− 6 Find the equation of the line tangent to the graph of f(t) at t = 8. Enter the equation of the tangent line here (in terms of the variable t): 
Calculus
Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the following equation of f '(x). f '(x) = y0 − y/x0 …