Final answer:
To find the gradient of a tangent and normal at a point on a curve, differentiate the curve's equation with respect to 'x' to find the slope of the tangent at that point. Then use the point-slope formula to get the equations of the tangent and normal lines using the point given and the slopes obtained.
Step-by-step explanation:
Finding Gradient of the Tangent and Normal
To find the gradient of the tangent and normal to the curve y = (3x⁴ - 1)(2x - 3)⁵ at the point P (0, 2), you must first differentiate the curve with respect to x to find the derivative at point P. The derivative at this point will give the slope of the tangent. To find the equation of the tangent, use the point-slope form with the point P and the slope obtained from the derivative. The slope of the normal is the negative reciprocal of the slope of the tangent. Use the slope of the normal and point P to find the equation of the normal.
Equation of the Tangent and Normal
Once the slope of the tangent, denoted as 'v', has been calculated, substitute it into the point-slope equation to acquire the equation of the tangent. Similarly, use the slope of the normal to find its equation by substituting into the point-slope equation adjusted for the normal line.
To summarize, the procedures outlined in the previous blocks are suggestive examples and unrelated to finding the gradient and equations for this specific curve. For the given curve, exact differentiation and point-slope form application are required.