Find if and the tangent line at ( x , f ( x ))has the slope.

Question

Find  if  and the tangent line at ( x , f ( x ))has the slope.

Quizplus · Accepted Answer

The last four digits of the four options are as follows:
Option A: 4bcbe560f748
Option B: 69751e87dc61
Option C: 15943c61dbd6
Option D: e341ecd737ac
Option E: 99df18c28666

We know that the only difference between the given number 11ebfe6a_2ce1_3ffe_96cc_7fb6c9d3b523_TBX8650_11 and the one we need to find is in the fourth-last digit, which changes from 'e' to 'f' to 'ff' to 'fff'. This suggests that the property of interest is related to the fourth derivative of the function.

The fact that the tangent line at (x,f(x)) has the slope 11ebfe6a_2ce1_3fff_96cc_77665728e507_TBX8650_00 means that the fifth derivative of the function at x is 11ebfe6a_2ce1_3fff_96cc_77665728e507_TBX8650_00. Therefore, the fourth derivative of the function at x must be obtained by differentiating this value with respect to x.

We can eliminate Options A, B, D, and E because the fourth-last digit in each of these options is even, whereas we need an odd digit (which represents the fourth derivative of an odd function at x). Therefore, the answer is Option C, which has the required '3' as the fourth-last digit.

Find If and the Tangent Line at