Question

In c++

This question is relevant if you implemented a polynomial that included some calculus-based operations such as derivative and integral. Write a new function that meets the following specification:

double slope(const polynomial& p, double x)

// POSTCONDITION: The return value is equal to the slope of the

// polynomial p, evaluated at the point x.

Answer 1

Solution:

In this question, we have to write the function which returns the slope of a given polynomial. so, here we calculate the differential calculus.
The formula for differential calculus is as follows:

If f(x) = axⁿ then, f'(x) = f(x) dx = a*nx^n-1 where n>=0 and a is coefficient (a>=1) .

Suppose f(x) = 2x²+4x. and x =2.

Then the slope will be f'(x) = 2x² dx + 4x dx
f'(x) = 2*2 x^2-1 + 4x^1-1
f'(x) = 4x + 4
put x = 2,
f'(2) = 4 * 2 + 4 = 8 + 4 = 12. (Slope of the polynomial) .  

C++ Function:

// the term_calulate function calculate the derivative of each term of polynomial.

double term_calulate(string pTerm, double val)
{
   // Get coefficient
   string coeffStr = "";
   int i;
   for (i = 0; pTerm[i] != 'x'; i++)
       coeffStr.push_back(pTerm[i]);
   double coeff = atol(coeffStr.c_str());

   // Get Power after skipping 2 characters for x and ^
   string powStr = "";
   for (i = i + 2; i != pTerm.size(); i++)
       powStr.push_back(pTerm[i]);
   double power = atol(powStr.c_str());

   // For ax^n, we return a(n-1)x^(n-1)
return coeff * power * pow(val, power - 1);
}

// The slope function takes the polynomial and value of point x as input and return the slope value as output.

double slope(string& poly, double x)
{
   double ans = 0.0;

   // Use istringstream to get input in tokens
istringstream is(poly);

   string pTerm;
   while (is >> pTerm) {

       // If the token is '+' then continue with the string
       if (pTerm == "+")
           continue;

       // Else find the derivative of particular term
       else
           ans = (ans + term_calulate(pTerm, x));
   }
   return ans;
}

Here we use the 2 functions the first function calculates the derivative of each term and the second one calculate the slope of the polynomial.