finding c: calc
posted by david .
let f(x)=square root x. if the rate of change of at x=c is twice its rate of change at x=1, then c=?
what???? i don't get get it.
to begin with, i took the derivative if that helps which is 1/(2*sqrtx) .
f'(x) = 1/(2*sqrtx) is correct
f'(x=1) = 1/2
The problem is to find the value of a constant x=c such that the derivative is twice the value at x=1, or 1.
f'(c) = 1 = 1/(2*sqrt c)
2 sqrt c = 1
sqrt c = 1/2
c = 1/4.

5 trillion
Respond to this Question
Similar Questions

calculus (rate of change)
consider the function f(x)=x^26x+12 a. find the average rate of change over the interval [1,3] b. use the definition of the derivative to find f prime(x) c. find the instantaneous rate of change at the point where x=3 d. find the … 
Calc
The wind chill is the temperature, in degrees Fahrenheit, a human feels based on the air temperature, in degrees Fahrenheit, and the wind velocity (v), in miles per hour (mph). If the air temperature is 32degrees Fahrenheit, then the … 
Calculus Please Help
Given the numerical values shown for the function f(x), find approximate values for the derivative of f(x) at each of the xvalues given. x= 0 1 2 3 4 5 6 7 8 f(x)= 13 15 16 17 17 14 11 9 7 f'(x)= 2 1 1 1 0 3 3 2 2 What seems to … 
Math
Could someone help me with these questions, I don't know question c) and d) Consider the function f(x) = (0.1x1)(x+2)^2. a) Determine the function's average rate of change on 2<x<6. Answer; Avg rate of change is 3.2 b) Estimate … 
Math~Reinyyy
Could someone help me with these questions, I don't know question c) and d) Consider the function f(x) = (0.1x1)(x+2)^2. a) Determine the function's average rate of change on 2<x<6. Answer; Avg rate of change is 3.2 b) Estimate … 
Calculus
for f(x)=x^2 +1, which value is the largest magnitude? 
calculus
The length l of a rectangle is decrasing at a rate of 5 cm/sec while the width w is increasing at a rate of 2 cm/sec. When l = 15 cm and w = 7 cm, find the following rates of change: The rate of change of the area: Answer = cm^2/sec. … 
Math
Hello, I'm supposed to do the following questions for the equation y=cos(pi/3)x for intervals [0,6] a) For what values of x does the instantaneous rate of change appear to equal 0? 
Algebra1
Can you check my answers? 1. Table modeling a linear relationship is shown below. What is the rate of change of nails to birdhouses? 
math
An investment of 25,000 earns interest at an annual rate of 8.4% compounded continuosly a. find the instantaneous rate of change of the amount in the account after years b. find the instantaneous rate of change of the amount in the …