Second Derivative \Help

In calculus (a branch of mathematics) the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity. The process of finding a derivative is called differentiation. Second derivative is higher derivatives of the function. (Source: Wikipedia) 

Example problems for second derivative help

Second derivative help example problem 1:
      Find the second derivative of the given function f (x) = 5x⁴ + 24x³ + 6.
Solution:
 Given function is f (x) = 5x⁴ + 24x³ + 6
Differentiate the given function with respect to x, we get
                           f'(x) = 20x³ + 72x²
Again differentiate the above function with respect to x, we get
                           f''(x) = 60x² + 144x
Answer:
  Second derivative value is f''(x) = 60x² + 144x
Second derivative help example problem 2:
      Find the second derivative of the given function f (x) = 12x² + 3x + 7.
Solution:
 Given function is f (x) = 12x² + 3x + 7
Differentiate the given function with respect to x, we get
                          f'(x) = 24x + 3x
Again differentiate the above function with respect to x, we get
                         f''(x) = 24
Answer:
  Second derivative value is f''(x) = 24
Second derivative help example problem 3:
      Find the second derivative of the given function f (x) = 6x³ + 5x²
Solution:
 Given function is f (x) = 6x³ + 5x²
Differentiate the given function with respect to x, we get
                          f'(x) = 18x² + 10x
Again differentiate the above function with respect to x, we get
                          f''(x) = 36x + 10
Answer:
  Second derivative value is f''(x) = 36x + 10

Practice problems for second derivative help

Second derivative help practice problem 1:
      Find the second derivative of the given function f (x) = 4x⁴ + 14x³
Answer:
  Second derivative value is f''(x) = 48x² + 84x
Second derivative help practice problem 2:
      Find the second derivative of the given function f (x) = 2x² - 56x
Answer:
  Second derivative value is f''(x) = 4
Second derivative help practice problem 3:
      Find the second derivative of the given function f (x) = x³ - 83x²
Answer:
  Second derivative value is f''(x) = 6x - 166