Maths-
General
Easy

Question

The slope of the tangent to the curve y equals 6 plus x minus x to the power of 2 end exponent at left parenthesis 24 right parenthesis is

  1. 10    
  2. fraction numerator 1 over denominator 3 end fraction    
  3. negative 3    
  4. negative 7    

hintHint:

We are given a curve. We have to find the tangent at the given point. To find the tangent, we will differentiate the equation w.r.t x.

The correct answer is: negative 3


    The given curve is y = 6 + x + x2.
    We have to find the slope tangent at point (2,4)
    To find the slope we differentiate the curve w.r.t x.
    table attributes columnalign left end attributes row cell y equals 6 plus x minus x squared end cell row cell fraction numerator d y over denominator d x end fraction equals 0 plus 1 minus 2 x end cell end table
    Slope m = open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis 2 comma 4 right parenthesis end subscript
    m = (1 - 2 × 2)
    = 1 - 4
    = -3
    The slope of the tangent at given point is -3.

    To find the slope we differentiate the given curve w.r.t x.

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