`y = x^4 - 3x^2 + 2, (1,0)` (a) Find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the derivative feature of a graphing utility to confirm your results.
Take the derivative of this function.
`y' = 4x^3-6x`
Substitute the value of x=1 from the given point into the derivative function.
`y' = 4(1)^3-6(1)`
`y'=4-6 = -2`
The slope at the given point is negative 2.
Graph the derivative function :
The derivative at x=1 is negative 2.
b) Our slope is -2, and we will use the slope-intercept form with the given point to find the y-intercept, and write our equation.
Substitute the point and slope.
`0 = (-2)(1)+b`
The equation of the tangent line is then:
The original function and the tangent line are graphed in the imaged attached.