pre calc

posted by .

why does x^4+7 and x^4 have the same derivative, meaning can someone explain to me why they are both equal to the derivative 4x^3?

  • pre calc -

    The derivative is SLOPE of the curve at x
    It does not matter if you move the graph of the function up 7 units, the slope will be the same at each x. Graph it :)

  • pre calc -

    a. Both have the exact same shape of curve, that is, except for position. Derivative means the function which defines the slope at any x, and both functions are the same.

    go to your definition of derative.\

    Lim d>0 of (f(x+d)-f(x))/d
    = Lim d>0 of ((x+d)^4 -x^4)/d
    = lim d>0 of (x^4+4x^3*d + ....-x^4)/d
    = lim d>0 of (4x^3d + higher terms of d)/d
    = 4x^3

    Now do the same for f(x)=x^4+7
    hint: the lim f(x+d)= (x+d)^4+7
    and if you work that it shortly becomes the same as above.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc

    a) y =ln(x-1) find dy/dx=? b) y=3 ln x - ln (1/x) where x >0, dy/dx= ?
  2. Pre-cal

    Hi, I don't understand this problem also. Find the the relative maximmum and minimum of x^3 - 6x^2 + 15. I'm supposed to do it using a graphing calculator but I still don't see any "lows" or "highs". Relative max and mins will occur …
  3. calc

    derivative of (x^3/6)+(1/2x)? i got (x^2/2)-(1/2x^2) is that correct?
  4. Calculus--> bobpursley

    How do you get m=0? from taking the second derivative?
  5. Derivatives- Math

    Can someone explain how to find the derivative of : 1. y= 5^ãx / x And the second derivative of: y= xe^10x For this question I got up to the first derivative and got this y = e^10x + 10xe^10x but I can't seem to get the correct …
  6. Calc-please help!

    What is the second derivative of (x^3)/(x^2-1)?
  7. Calc

    Set the first derivative and second derivative of x^2/x-2 equal to 0. Solve for 0.
  8. Calc-Derivative

    Find the derivative of x^(1/x). Can someone show me steps for this problem...I go round in circles
  9. Calc

    sinx+x^2y=1 use implicit differentiation to find the second derivative. For the first derivative I got (cos(x)+2xy)/x^2. I have a feeling that is wrong, can someone please help and show steps on how to do this problem. (studying for …
  10. Math

    what value of x is the derivative of x^3 is equal to the derivative of x^2 + x?

More Similar Questions