Let f ( x ) = 1 4 x 3 + 12 x + 6 and let y = f − 1 ( x ) be the inverse function of f. Determine the x-coordinates of the two points on the graph of the inverse function where the tangent line is perpendicular to the straight line y = − 24 x − 32.

Question

Let   f  (  x  )  =      1    4        x    3    +  12  x  +  6 and let   y  =      f          −      1        (  x  ) be the inverse function of   f. Determine the   x-coordinates of the two points on the graph of the inverse function where the tangent line is perpendicular to the straight line   y  =  −  24  x  −  32.

partyjnopp9wa · Accepted Answer

y  =      1    4        x    3    +  12  x  +  6  L  =  −  24  x  −  32  P  is a line that is perpendicular to   L.The slope of a perpendicular is the negative of the multiplicative inverse, that is:            d      P              d      x        =  −  (            d      L              d      x            )          −      1        =  −            d      x              d      L      To solve the problem we want   y where:                                          d            x                                d            y                          ⏟                    slope of the inverse        =                                          d            P                                d            x                          ⏟                    Slope of a perpendicular                  d      x              d      y        =  −            d      x              d      L                  d      y              d      x        =  −            d      L              d      x            3    4        x    2    +  12  =  −  (  −  24  )  x  =  ±  4Then just find the corresponding   y values, which are the   x values of the inverse function.

Let f ( x ) = 1 4 </mfrac> x 3 </msup> + 12

Answered question

Answer & Explanation

New Questions in Differential Calculus