calculus
posted by Anonymous .
determine the slope of the tangent for the following function. Then determine the equation of the tangent line at x=1
F(x) = x
F(x) = x^4

For F(x) = x, the first derivative  which is the slope of the line tangent to a curve  would be:
F'(x) = 1
For the second part, it doesn't matter what value x is, F'(x) is always 1.
For F(x) = x^4, the first derivative  which is the slope of the line tangent to a curve  would be:
F'(x) = 3x^3
For the second part, you just plug in 1 for x:
F'(x) = 3(1)^3 = 3 
HOLD ON!!! MY BAD!
The second function's derivative is wrong. Brain fart on my part.
For F(x) = x^4, the first derivative  which is the slope of the line tangent to a curve  would be:
F'(x) = 4x^3
For the second part of the question, you just plug in 1 for x:
F'(x) = 4(1)^3 = 4
Respond to this Question
Similar Questions

calculus
Determine the slope of the tangent m, for each of the following functions. Then determine the equation of the tangent line at x=1. a) f(x) = 1/ sqrt of x b) f(x) = 60  5t^2 
calculus
Determine the slope of the tangent m, for each of the following functions. Then determine the equation of the tangent line at x=1. For f(x) = 1/x^3 
Calculus
Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 7 x  2 x^2 text( at ) \(1,9\) m = y = 
Calculus PLEASE HELP
Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 2 x  4 x^2( at ) (2,20) m= y= 
Calculus
consider the function y = 2sinx a) determine dy/dx b) calculate the exact value of x for which the slope of the tangent to the graph is √2 in the interval [0, pie] c) determine the equation of the tangent in part (b). d) determine … 
Applied Calculus......
Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=6x5x^2 at (2, 32) I have to use the four step process, but seem to be getting stuck... 
Calculus
Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/4 x at (1,15/4) 
Calculus
Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/(4 x) at (1,(15/4) m = y = 
calculus
Use the fourstep process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2  5x +2 (1, 2) 
Calculus
Use the fourstep process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 2x22x+1 (1, 2)