FIND THE TANGENTS TO THE CURVE Y=2X^3+3X AT THE POINTS WHERE THE SLOPE IS 9. WHAT IS THE SMALLEST SLOPE ON THE CURVE? AT WHAT VALUE OF X DOES THE CURVE HAVE THIS SLOPE?? PLEASE HELP AND SHOW ALL STEPS!

Question

anonymous · Answer

WELL FIRST DIFFERENTIATE THE FUNCTION WITH RESPECT TO X AND SOLVE TO FIND AT WHAT X VALUE THE SLOPE IS EQUAL TO 9.

anonymous · Answer

THEN, FIND THE Y-VALUE OF THE ORIGINAL FUNCTION AT THAT X-VALUE, AND USE THE POINT-SLOPE FORM OF A LINE TO DETERMINE THE EQUATION FOR THE TANGENT LINE.