+4 a.Given the polynomial function y = 1/5x⁵ + 1/4x⁴ - 7/3x³ - 1/2x² + 6x
a. Use the definition of derivative to differentiate y = 1/5x⁵ + 1/4x⁴ - 7/3x³ - 1/2x² + 6x
b. Find the points on the graph where the tangent line is horizontal and the equation of the tangent line at the points. Draw these points and lines on the graph of the function.
c. Find the equation of the tangent line and the normal line to the graph of the function at a point where:
x = 0
d. Draw the graph of the function on [ - 7/2 , 5,2 ] and the equation of the tangent and normal lines at the given value of x
-7/2 -3 -5/2 -2 -3/2 -1 -1/2 0 1/2 1 3/2 2 5/2
y = 1/5x⁵ + 1/4x⁴ - 7/3x³ - 1/2x² + 6x
Decimal/ Approximate value
[2 decimal places]
