calculus 2
posted by rimmel .
Suppose that you can calculate the derivative of a function using the formula f'(x) = 4f(x) + 2x. If the output value of the function at x= 4 is 2 estimate the value of the function at 4.013

calculus 2 
drwls
I would estimate it using the first two terms of a McLaurin series expansion:
f(4.013) = f(4) + (4.0134) f'(x)
= f(4) + 0.013 f'(4)
where f(4) = 2, and
f'(4) = 4f(4) + 2*4 = 16
So, f(4.013) = 2 + 0.013*16 = 2.208
Respond to this Question
Similar Questions

Calculus
Suppose that you can calculate the derivative of a function using the formula f(x) = 2f(x) + 4x. If the output value of the function at x=4 is 3 estimate the value of the function at 4.012. Linear Approximation right? 
calculus
I have three questions I'm having a terrible time with: 1)Find, if possible, the absolute maximum value and where it occurs for f(x)=ln(xe^x) on (0,infinity). 2)Find the value(s) of "c" guaranteed by the Mean Value Theorem for the … 
Calculus
I finished this problem but I wanted some feedback because I don't know if it's entirely correct. Suppose that functions f and g and their derivatives with respect to x have the following values at x=2. f(x)=8 g(x)=2 f'(x)=1/3 g'(x)=3 … 
calculus
is the function f(x)=x^2 increasing on decreasing at x = 1. can anyone please check my reasoning: the value of the derivative of the function at x=1 is 2, so that means the slope of the tangent line to the graph at that is a negative … 
Calculus
Find the linear approximation L(x) of the given function at a, and use it to approximate the function value at the given xvalue. f(x)=x^(1/3), a=27, x=28 I found the derivative to be f'(x)= 1/[3(27)^(2/3)] but it does not exist … 
Calc. checking answer
Determine whether or not each of the following functions is invertible. Give your reasons for believing the function is invertible or not. Please check this for me. I am not sure if I am adequately explaining my answer and if my answer … 
Math Calculus
Economists use production functions to describe how output of a system varies with another variable such as labour or capital. For example, the production function P(L) = 200L + 10L^2  L^3 goves the output of a system as a function … 
calculus please help asap
true or false questions: a)The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. b) A sinusoidal function can be differentiated only if the independent variable … 
Calculus
Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^1 (9))'[the derivative of … 
Calculus
f'(x)=sqrt(x)*sin(x) The first derivative of the function f is given above. If f(0)=0, at which value of x does the function f attain it's minimum value on the closed interval [0,10]?