5. (4 pts) Fill in the blank in each sentence below to describe a feature on a slope graph given a feature on its corresponding function graph. Choose from: "be increasing", "be decreasing", "lie above the x -axis", or "lie below the \( x \)-axis", "zero", "positive", "negative", "relative max or min", "inflection point", "vertical asymptote", "herizontal asymptote". "bole", "jump" a) If a continuous and differentiable function \( f(x) \) has a relative minimum at \( x=1 \), then its slope graph must have a/an \( \qquad \) at \( x=1 \). b) If a continuous and differentiable function \( g(x) \) has an inflection point at \( x=-2 \), then its slope graph must have a/an \( \qquad \) at \( x=-2 \). c) If a continuous function \( h(x) \) has a vertical tangent at \( x=0 \), then its slope graph has \( \qquad \) at \( x=0 \). d) If a continuous and differentiable function \( j(x) \) is decreasing on the interval \( (0,10) \), then its slope graph must \( \qquad \) on the interval \( (0,10) \). e) If a continuous and differentiable function \( j(x) \) is concave up on the interval \( (0,10) \), then its slope graph must \( \qquad \) on the interval \( (0,10) \).
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a) If a continuous and differentiable function \( f(x) \) has a relative minimum at \( x=1 \), then its slope graph must have a/an **relative max or min** at \( x=1 \). b) If a continuous and differentiable function \( g(x) \) has an inflection point at \( x=-2 \), then its slope graph must have a/an **zero** at \( x=-2 \). c) If a continuous function \( h(x) \) has a vertical tangent at \( x=0 \), then its slope graph has **a jump** at \( x=0 \). d) If a continuous and differentiable function \( j(x) \) is decreasing on the interval \( (0,10) \), then its slope graph must **be decreasing** on the interval \( (0,10) \). e) If a continuous and differentiable function \( j(x) \) is concave up on the interval \( (0,10) \), then its slope graph must **be increasing** on the interval \( (0,10) \).
