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1.7 Differentiation

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Question 105

The mechanical stress, yyy, on a structural beam is modeled by the function y=1.5(2x−7)4+18y = 1.5(2x - 7)^4 + 18y=1.5(2x−7)4+18, where xxx is the beam's temperature in degrees Celsius. The curve of this relationship passes through the point (3.5,18)(3.5, 18)(3.5,18).

By differentiating the function using the chain rule, determine the equation of the normal to the curve at the point (3.5,18)(3.5, 18)(3.5,18).

Select your answer from the options below:

y=18 y = 18 y=18 y=3.5 y = 3.5 y=3.5 x=18 x = 18 x=18 x=3.5 x = 3.5 x=3.5
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Markscheme

1.7 Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.7 Differentiation

425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

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