Calculus Word Problems

How to Solve Word Problems in Calculus

We will  introduce some word problems in calculus.

1. Find the velocity  of  the car which as to travel a distance  given by the equation  y= x² - 5x + 6 at the tine t = 5 sec.

Step  1 : First find the distance of the car traveled by differentiating it
              $\frac{d}{dx}$ (  x²-5x+6)
             y1=  2x - 5
            y1=  2(5) - 5
               = 10 - 5
               = 5 m

2. Find the acceleration  of the body  y= x³ - 2x at x = 1m

Step 1

First find the derivative for the above equation
Y1 = 3x² - 2

Y2 = 6x
   =  6(1)
  =6 m/sec2.

3. Find  the equation of the tangent  and normal to the curve y= 2x² + 4x - 3 at ( -2,-3)
Y= = 2x² + 4x - 3  

 $\frac{dy}{dx}$ = 4x + 4
           =  4(-2) + 4
          = -8 + 4
         =  -4  at (x y)

Step1
Now  the  equation of  tangent is  given  by  y - y₁ = m(x - x₁)
y - (-3) = -4(x - (-2))
y + 3 =  -4x -  8
y + 3 + 4x + 8 = 0
y + 4x + 11 = 0

Now   to  find  the equation of normal  is given by     y-y₁=-m(x-x₁)
   y-(-3) = -$\frac{1}{4(x-(-2))}$
4y + 3 = -x - 2
4y + x + 5 = 0  is the  equation of the normal